Method and tool for determination of fracture geometry in subterranean formations based on in-situ neutron activation analysis

ABSTRACT

A method for determining fracture geometry of a subterranean formation from radiation emitted from a fracture in the formation, including measuring gamma-radiation emitted from the fracture; subtracting background radiation from the measured gamma-radiation to obtain a peak-energy measurement; comparing the peak-energy measurement with a gamma-ray transport/spectrometer response model; and determining formation fracture geometry of the fracture in accordance with values associated with the response model.

CROSS-REFERENCE TO RELATED APPLICATION AND CLAIM OF PRIORITY

This application is a continuation-in-part of co-pending applicationSer. No. 11/501,575 filed Aug. 9, 2006, which is incorporated herein byreference in its entirety.

FIELD OF THE INVENTION

The present invention relates to methods for determining fracturegeometry in subterranean formations, such as found in bored wells foroil and natural gas production.

BACKGROUND OF THE INVENTION

The yield of hydrocarbons, such as gas and petroleum, from subterraneanformations can be increased by fracturing the formation in order tostimulate the flow of these hydrocarbons in the formation. Variousformation fracturing procedures are now used, such as, for example,hydraulic fracturing in which liquids, gases and or combinations of bothare injected into the formation under high pressure (usually withpropping agents).

Hydraulic fracturing is often used in the industry for improving oil andnatural gas production from subterranean formations. During a hydraulicfracturing operation, a fluid, generally termed a “pad,” is pumped downa well at sufficient pressure to crack or fracture open the formationsurrounding the well. Once a fracture has been created, the pumping ofthe pad, along with a slurry phase that comprises both the liquid and aproppant, is begun until a sufficient volume of the proppant has beencarried by the slurry into the fracture. After a suitable time, thepumping operation is stopped at which time the proppant will prop openthe fracture in the formation, thereby preventing it from closing. As aresult of the fracture, trapped hydrocarbons are provided a moreconductive pathway to the wellbore than was previously available,thereby increasing the well's production. In addition to creatingdeep-penetrating fractures, the fracturing process is useful inovercoming wellbore damage, to aid in secondary operations and to assistin the injection or disposal of produced formation brine water orindustrial waste material.

During the fracturing process, the fractures propagate throughout theformation. The vertical propagation of these fractures is useful indetermining the extent of fracture coverage as it relates to theproducing interval. Fracture height measurements aid well operators indetermining the success of the fracturing operation and, if necessary,to optimize future treatments for other wells in the field. In addition,fracture height information can aid in the diagnosis of stimulationproblems such as lower production rates or unfavorable water cuts. Thefracture height data can indicate whether communication has beenestablished between the producing formation and adjacent water ornon-hydrocarbon producing formation zones. Height measurements alsoprovide a check on the accuracy of fracture design simulators used priorto the job to predict fracture geometry. If excessive fracture heightgrowth is determined this would imply that the fracture length isshorter than the designed value.

As stated above, one reason for monitoring the vertical propagation of afracture is the concern for fracturing outside of a definedhydrocarbon-producing zone into an adjacent water-producing zone. Whenthis occurs, water will flow into the hydrocarbon-producing zone and thewellbore, resulting in a well that produces mainly water instead of thedesired hydrocarbon. Furthermore, if there is still the desire tocontinue producing hydrocarbons from the well, operators must solve theserious problem of safely disposing of the undesired water. Addressingthe problems arising from an out-of-zone fracture will also add expensesto the operation. In addition, if the fracture propagates into anadjacent non-hydrocarbon producing formation, the materials used tomaintain a fracture after the fluid pressure has decreased may be wastedin areas outside the productive formation area. In short, it isexpensive to efficiently operate a well that has been fractured out ofthe hydrocarbon-producing zone.

Because of the serious problems that can occur as a result ofout-of-zone fractures, it is desirable to determine formation fracturedevelopment. Several techniques and devices are known for monitoring andevaluating formation fracture development, such as radioactive tracersin the fracturing fluid, temperature logs, borehole televiewers, passiveacoustics and gamma-ray logging. Most techniques provide some directestimates of fractured zone height at the wellbore.

One known process used to determine formation fracture heightdevelopment employs a radioactive tracer. In this process, a fracturingfluid containing a radioactive tracer is injected into the formation tocreate and extend the fractures. When these radioactive fluid andproppant tracers are used, post fracture gamma-ray logs have shownhigher levels of activity opposite where the tracer was deposited,thereby enabling operators to estimate the vertical development of thepropped fractures.

Another approach for determining fracture height uses temperature andgamma-ray logs. Temperature logs made before and after stimulation arecompared to define an interval cooled by injection of the fracturingfluid and thus provide an estimate of the fractured zone. However, thistechnique is subject to limitations and ambiguities. For example, thetemperature log may be difficult to interpret because of low temperaturecontrast, flowback from the formation before and after the treatment, orfluid movement behind the borehole casing. In addition, the use ofradioactive tracers may give rise to environmental problems such as thepollution of underground water streams, and the like, and hence beundesirable.

Other known methods for evaluating fracture geometry include using aborehole televiewer or using acoustical methods. Utilizing a boreholeteleviewer is limited in that it can only be used for fracture heightevaluation in open holes. In addition, utilizing a borehole televieweris limited due to the extreme temperature and pressure conditionspresent in deeper completions. Acoustical methods are hampered byinhomogeneous formation impedance and/or the need for pumping while thetool is in the wellbore.

In addition to the problems associated with each type of knownmonitoring method, there are inherent problems in the formationfracturing technology. During the fracturing process, fracture fluid isgenerally pumped into the formation at high pressure, to force open thefractures, and an increasing proportion of sand is added to the fluid toprop open the resulting fractures. One problem with the existingtechnology is that the methods for determining whether a formation hasbeen fractured out of the production zone relies on post-treatment (i.e.after the fracture has occurred) measurements. In such systems, afracturing treatment is performed, the treatment is stopped, the well istested and the data is analyzed. Moreover, with existing detectionsystems, the wait for post-fracturing data can take a considerableamount of time, even up to several days, which can delay the completionoperations, resulting in higher completion and operating costs.

Another problem associated with existing post-process “logging” ormeasuring devices is that the cost associated with interrupting afracturing job in order to make a measurement of a fracture is neitherpractical nor feasible. Because the fracturing fluid is pumped into aformation under high pressures during the fracturing process,temporarily halting the pumping during the fracturing operation willresult in the application of pressure to the fracturing fluid by thewalls of the formation fracture. This could lead to undesirable resultssuch as the closing of the fractures, thereby causing the reversal offluid flow back into the borehole, or the build-up of sand in the hole.In addition, after taking measurements and completing the loggingprocess, operators cannot restart the pumping equipment at the point ofthe fracturing process immediately before the interruption. Instead, theoperators would have to repeat the complete fracturing job at additionalcost and with unpredictable results.

A fracture monitoring system that does not require interrupting afracturing job could address the above-described problems and wouldallow well operators to monitor the fracturing process, to controlfracture dimensions and to efficiently place higher concentrations ofproppants in a desired formation location. In addition, if there isinformation that a fracture is close to extending outside the desiredzone, operators can terminate the fracturing job immediately.Furthermore, analysis of the ongoing treatment procedure will enable anoperator to determine when it is necessary to pump greaterconcentrations of the proppant, depending on factors such as thevertical and lateral proximity of oil/water contacts with respect to thewellbore, the presence or absence of water-producing formations andhorizontal changes in the physical properties of the reservoir rock.

SUMMARY OF THE INVENTION

The present invention solves the existing problems in the art byproviding a method for analyzing the results of a fracturing process bycollecting and analyzing well logging data, comprising disposing in aformation fracture, a proppant and/or a fracturing fluid that comprisesa radiation susceptible material; during a single logging passirradiating the radiation susceptible material with neutrons; measuringgamma-radiation emitted from the radiation susceptible material; andprocessing the measured gamma-radiation data in accordance with a MonteCarlo-based simulation model to obtain an estimated fracture geometry(e.g. propped height and/or propped fracture width near the wellbore).

In accordance with embodiment, a method is provided for modelinggeometrical parameters of a proppant filled fracture in a subterraneanformation detected by collecting gamma-radiation data stimulated by aneutron source, including obtaining neutron transport data by applyingneutron source parameters and subterranean formation parameters to aMonte Carlo simulation; obtaining gamma-ray buildup/decay profile databy integrating said neutron transport data; generating a gamma-raytransport/spectrometer response model by applying a Monte Carlosimulation to said gamma-ray buildup/decay profile data; and creating agamma-ray transport/spectrometer response database correlatinggamma-radiation spectra with subterranean formation proppant filledfracture geometry parameters. We also rely on the ability to generatespectrometer response data by MC simulation from other nuclides whichbecome activated in the irradiation. That data is needed to determinewhat contribution from the experimentally observed spectrum is not fromthe tag, and therefore to isolate from the complex spectrum the partthat is from the activation of the tag.

In accordance with another aspect of the invention, a method is providedfor determining fracture geometry of a subterranean formation fromradiation emitted from a fracture in said formation, including measuringgamma-radiation emitted from the fracture; subtracting backgroundradiation from said measured gamma-radiation to obtain a peak-energymeasurement; comparing said peak-energy measurement with a gamma-raytransport/spectrometer response model; and determining formationfracture geometry of said fracture in accordance with values associatedwith said response model. First, all radiation is measured. Backgroundfrom the upper detector is subtracted, then interfering signatures fromother activation products are accounted for to determine the tag'scontribution. When the tag's contribution is known, it can be related tothe amount of proppant present and thus to the fracture width. Theobserved spectrum is seen as a combination of signature spectra, whereeach activation product (including but not limited to the tag) has itsown signature. This ‘signature’ approach is what we call Library LeastSquares, and we call the ‘signatures’ Library Spectra. The libraryspectrum for the tag has been quantitatively indexed by applying thewhole NT/RBD/GRT-DR simulation, so that the result of the Library LeastSquares provides a quantitative estimate of most likely tagconcentration which would have produced that observed spectrum.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts an exemplary embodiment of a proppant comprising a solidcore upon which is disposed an organic coating that comprises aradiation susceptible material in accordance with the invention;

FIG. 2 depicts an exemplary well logging tool for use with the methodand proppant of the present invention;

FIG. 3 depicts a block diagram of a method for analyzing measuredneutron activation data from a well fracture in accordance with anembodiment of the present invention; and

FIG. 4 depicts a cross-sectional view of a three-dimensional input to aneutron transport calculation model in accordance with the method of thepresent invention.

DETAILED DESCRIPTION OF THE INVENTION

In accordance with the present invention, a method for determiningfracture geometry uses environmentally friendly materials. Theseenvironmentally friendly materials are nonradioactive until bombarded byneutrons and will be referred to as radiation susceptible materials. Inone embodiment, the method involves determining the geometry (i.e.aspects of proppant packed height and width) of a fracture created in aformation using target elements that comprise the radiation susceptiblematerials. The radiation susceptible materials have a short half-life,which advantageously permits them to be used in a formation while at thesame time minimizing any adverse environmental impact, either fromhandling or having the proppant flow back out of the well either duringclean-up or when the well is put back on production.

Radiation susceptible materials as defined herein are those that becomeradioactive upon bombardment by neutrons. The radiation susceptiblematerials can advantageously be disposed in the fracturing fluid, or ina coating disposed upon a proppant that is disposed in the fracturingfluid or as a part of core of the proppant itself. The fracturing fluidor the proppant that comprises the radiation susceptible material can beused during a hydraulic fracturing treatment. The fracturing fluidand/or the proppants that comprise the radiation susceptible materialsare injected into the formation during the creation of the fracture.After being injected into the fracture, the radiation susceptiblematerials are irradiated with neutrons from a neutron source containedin a logging tool. Gamma radiation emitted from the radiationsusceptible materials is counted by detectors contained in the loggingtool. Since the radiation susceptible materials have a short half-life,these materials become radioactive for only a brief period of time. Thelocation of the gamma radiation is used to determine the placement ofthe radiation susceptible materials in the fracture and is also used todetermine aspects of the proppant filled fracture geometry, such aspropped fracture height and propped fracture width.

Generally, the radiation detector generates a “spectrum” in the presenceof radiation of different energies, i.e. peak, scatter and background,as well as radiation of different isotopes. As a photon hits thedetector, its energy is converted to an electrical signal that isprocessed. Photons of different energies will generate electricalsignals of different values. The summation of these will result in anenergy spectrum. Generally, at least two of the detectors have thecapability to not only count the number of rays that hit the detectorbut also determine the energy level associated with that particularemission.

Typically a known and consistent concentration of the radiationsusceptible material (also termed a “tag”) is employed to facilitatecalculating a propped fracture width. Preferably, the tag could eitherbe in the coating or in the body of the proppant.

The present method is advantageous in that background radiation acquiredduring the activation of the radiation susceptible materials can becollected in a single pass and subtracted from the peak energyradiation. All other commercially available processes generally use twoor more logging passes to determine the fracture geometry of thefractured formation, where a first logging pass to measure background istypically performed before the fracturing treatment has begun, as theprior art uses radioactive tracers that are added to the proppant andthe fracturing fluid as the fracturing treatment is being performed, andthus once the proppant is present background could no longer bemeasured. The acquired background radiation generally comprises multiplecontributions from a number of sources. A first contribution cangenerally be acquired from naturally occurring radioactive elements suchas uranium, potassium, and/or thorium. Over time, fine-grainedformations can trap minerals and fluids containing these naturallyradioactive elements. When the radiation susceptible materials in theformation are activated by neutrons, these naturally occurringradioactive materials will also emit radiation, which is acquired asbackground radiation.

A second contribution to the background is that induced by neutronradiation being presently used to activate the radiation susceptiblematerials. This radiation emanates mainly from aluminum and siliconpresent in the formation and/or the proppant. Background radiation fromiron/manganese used in the wellbore casing may also be a part of thisthird contribution. In accordance with one aspect of the invention, thewell containing the radiation susceptible material that has been exposedto a neutron source is logged at an uncharacteristic slow rate, such ason the order of 2 feet per minute. Logging at this slower rate allowstime for any neutron-stimulated emissions from naturally occurringelements to decrease relative to the emissions from the radiationsusceptible tag. This helps in separating the energy peaks associatedwith naturally occurring elements from those of the radiationsusceptible tracer. This makes the analysis on the logging data easierand the results more accurate.

It is desirable to remove all traces of background radiation from thepeak energy radiation prior to calculation of fracture geometry. In oneembodiment, the peak energy radiation measurements as well as backgroundradiation measurements are made in a single pass, and the backgroundradiation measurements are subtracted from the peak energy radiationmeasurements in a single pass. This is preferably done by having twospectrum detectors in the logging tool. As explained below, the upperdetector is used to measure natural background radiation, while the toolshould be lowered as quickly as possible, though, to prevent muchactivation from occurring on the way down. This is particularly true forradioisotopes with long half-lives.

The radiation susceptible materials can be disposed in a proppant thatis introduced into the fracture to prop open the fracture. In oneembodiment, the proppant can comprise a substrate upon which is disposeda coating comprising the radiation susceptible material. In anotherembodiment, the substrate can comprise the radiation susceptiblematerial. When a proppant and/or fracturing fluid comprises a radiationsusceptible material, it is said to be tagged with the radiationsusceptible material. The term “tagging” as used herein implies that theproppant and/or the fracturing fluid comprises radiation susceptiblematerials. Thus, when a coating disposed on a substrate comprisesradiation susceptible materials, the proppant is said to be tagged witha radiation susceptible material.

FIG. 1 shows an exemplary embodiment of a proppant 10. The proppantcomprises a substrate 2 having a coating 4 disposed thereon thatcomprises the radiation susceptible material 6. The coating 4 cancomprise an organic or an inorganic material. The substrate 2 cancomprise an organic material and/or an inorganic material and/or ametal. The coating 4 can be uncured, partially cured or fully curedprior to use in a subterranean fracture. This curing can occur eitherinside and/or outside the subterranean fracture. Alternatively, theradiation susceptible material 6 can be disposed in the body of theproppant without a coating.

The coating 4 can optionally comprise particulate fillers or fibrousfillers 8 if desired. The proppant 10 comprises a metallic and/orinorganic substrate 2 that generally comprises a single particle or isan agglomerate comprising a plurality of particles. Examples of metalsthat can be used in the substrates are shape memory alloys. Shape memoryalloys exhibit a “shape memory effect”. The shape memory effect permitsa reversible transformation between two crystalline states i.e., amartensitic state to an austenitic state and vice versa. Generally, inthe low temperature, or martensitic state, shape memory alloys can beplastically deformed and upon exposure to some higher temperature willtransform to an austenitic state, thereby returning to their shape priorto the deformation.

A suitable example of a shape memory alloy is a nickel titanium alloysuch as NITINOL®. It is desirable for the shape memory alloys to befoamed. In one embodiment, a substrate manufactured from a shape memoryalloy can be a solid prior to introduction into the fracture, but canexpand into a foam after introduction into the fracture, which isgenerally at a higher temperature than the temperature above ground.This expansion will permit better conductivity of oil and gas from thefracture.

Naturally occurring organic and inorganic materials that aresubsequently modified can also be used as the substrate. Suitableexamples of organic and inorganic materials that are modified an used inthe substrate are exfoliated clays (e.g., expanded vermiculite),exfoliated graphite, blown glass or silica, hollow glass spheres, foamedglass spheres, cenospheres, foamed slag, sintered bauxite, sinteredalumina, or the like, or a combination comprising one of the foregoingorganic and inorganic materials. Exemplary inorganic substrates may bederived from sand, milled glass beads, sintered bauxite, sinteredalumina, naturally occurring mineral fibers, such as zircon and mullite,or the like, or a combination comprising one of the naturally occurringinorganic substrates. Hollow glass spheres can be commercially obtainedfrom Diversified Industries Ltd.

The radiation susceptible material that is included in the coating onthe substrate or in the substrate of the proppant is neutron-responsiveso that it readily reacts to neutrons, such as by absorbing thermalneutrons to exhibit a relatively large atomic cross section. By suchresponsiveness to neutrons, the radiation susceptible material yieldsthe characteristic gamma radiation or neutron absorption, which isdistinguishable from the characteristics of the materials in thesurrounding formation. These radiation susceptible materials are alsoinitially non-radioactive so that they can be safely handled withoutfear or risk of radiation exposure or contamination at the surface ofthe well until after it is introduced into the system by which it is tobe moved into the well. Such a material also will revert back to itsnatural (non-radioactive state) in a short period of time, such as onthe order of minutes after activation.

Although the radiation susceptible material is initiallynon-radioactive, the isotope of the radiation susceptible material isone which either becomes radioactive, whereby the created radioactiveisotope decays and emits gamma radiation detectable by a suitabledetector, or otherwise undergoes a nuclear or atomic reaction, such asby simply absorbing one or more neutrons to an extent greater than thematerials of the surrounding formation. Such a reaction can occur inresponse to the external neutrons emitted from an accelerator. If theoriginal substance is to react by forming a radioactive isotope, theradioactive isotope preferably has a known half-life of betweenapproximately a few seconds and up to about 30 minutes so that prolongedirradiation by the accelerator is not needed for the reaction to occurand so that adequate detection time exists once the conversion hasoccurred. It is advantageous that the susceptible material decays to anon-radioactive state shortly after the logging process is performed,thereby allowing the well to be brought back onto production withoutfear of producing radioactive material.

In one embodiment, the radiation susceptible materials have a half-lifeof about 5 seconds to about 20-30 minutes. In another embodiment, theradiation susceptible materials have a half-life of about 10 seconds toless than or equal to about 50 minutes. In yet another embodiment, theradiation susceptible materials have a half-life of about 12 seconds toless than or equal to about 7 minutes. An exemplary half-life for aradiation susceptible material is less than or equal to about 5 minutes.Vanadium has a half-life of 3.8 minutes, while indium has a half-life of14.1 seconds. It is generally desirable for the period of measurableradiation to be of a length so that the material no longer emitsradiation when the well starts producing hydrocarbons. In general, it isdesirable for the radiation susceptible material to stop emittingmeasurable radiation before it is placed back on production. It is alsoadvantageous in that after the half-life of the radiation susceptiblematerial has expired, the well can be re-logged as many times as desiredby re-irradiating the radiation susceptible material.

A suitable spectral gamma-ray logging tool may be utilized to measurethe gamma radiation obtained from the radiation susceptible materialafter it is bombarded by neutrons. At least a portion of the tool, e.g.,at least the gamma-ray detector, is placed within the well to providethe desired log. The tool can be such as to generate the desired ratiosdownhole, or the gamma-ray spectra can be transmitted to the surface andthe ratios determined from the spectral data. Either a low resolution,e. g., NaI(Tl) or equivalent, detector (such as BGO crystal) or a highresolution, e.g., intrinsic germanium, Ge(Li) or equivalent detector canbe used. NaI has some advantages that BGO does not in practicalapplication. This includes its temperature dependence for gain stabilityand its slightly better resolution whenever one needs to do qualitativeanalysis. By using the library least-squares (LLS) approach only thequalitative analysis requires detectors with good resolution so thatpeaks can be identified. Quantitative analysis by using the entirespectrum with the LLS approach is essentially independent of resolutionsince the accuracy of this approach depends only on the ‘overall shape’of the library spectra rather than the sharpness of the peaks. It isvery important that the detector be stable (with respect to time andtemperature) so that the collected counts are associated to the properenergy level. With the BGO detector this means putting the crystal in atemperature flask that is specifically design to maintain the crystal'stemperature in an optimum performance range throughout the loggingoperation. Logs can be generated either in a continuous, moving toolmode, or in a stationary mode in which the tool is stopped at selectedlocations in the borehole.

An example of a suitable logging tool is shown in FIG. 2. The toolincludes an upper spectral gamma-ray detector 21, a neutron source 22,and a lower spectral gamma-ray detector 23. A collimator can be used onthe detector if desired. In one embodiment, a rotating collimator isused to measure fracture orientation. Such collimators tend to increasethe sensitivity of the measurement since such devices reduce the numberof gamma rays entering the detector from locations up or down theborehole, i.e., gamma rays from proppant that is behind the casing butis above or below the current location of the detector. In oneembodiment, a detector without a collimator can be used.

In one method of determining fracture height, tagged proppants and/or atagged fracturing fluid are introduced into the formation. The taggedproppants and/or tagged fracturing fluid generally comprise indiumand/or vanadium, however other tags may be suitable as well. The taggedproppant and/or tagged fracturing fluid is then bombarded with neutronsfrom the neutron source 22 during a logging pass. A logging pass is onewherein the logging tool is introduced into the well and wherein aneutron bombardment of the formation fracture is initiated. Gamma rayspectroscopy is then performed on the irradiated radiation susceptiblematerial such as indium and vanadium to obtain gamma count rates bothabove and below the peak energies (also referred to as off-peakenergies) coming from vanadium and/or indium. Gamma count rates aremeasured at the peak energies for indium and/or vanadium as well. Inoperation, the upper spectral detector is used to measure backgroundradiation in the well prior to activation of the radiation susceptiblematerial. The entire spectrum (all energy emissions) is measured bothbefore and after exposure to the neutron source. The two measuredspectrums are then overlaid on each other peaks that are not zeroed outby the subtraction process are identified. After that, thecharacteristic energy level emissions of the tagging element areidentified.

In accordance with the present invention, analysis of the gammaradiation data collected by the logging tool is performed by applyingthe collected data to a simulation model system. As shown in FIG. 3, themodel system is based on three major components: a neutron transportmodel, a radionuclide buildup/decay model, and a gamma-raytransport/spectrometer response model.

The purpose of the model is to obtain neutron reaction rates as afunction of the position of the reactive material relative to theneutron source position. The reaction rates that are obtained are thosereactions where desired gamma-ray emitting nuclides are produced, inother words the production rates for any gamma-ray emittingradio-nuclides in which an analyst would be interested.

The neutron transport model is an important and potentially complexcomponent of the model system. Due to the nature of neutron transport, aMonte Carlo approach to the neutron transport problem is preferred, andin one embodiment of the invention the highly versatile and widely knownMonte Carlo N-Particle Transport Code, Version 5 (MCNP5) is used tomodel neutron transport behavior. The geometry and composition of thelogging tool is modeled in the vicinity of the neutron source in threedimensions, and the atomic composition of the borehole fluid and thesurrounding formation is also inputted into the simulation. A symmetricfracture is defined as an idealized slab containing a different atomiccomposition than the surrounding formation.

FIG. 4 illustrates a cross-sectional view of the three-dimensionalgeometric input to the neutron transport model. As shown, the inputincludes a tool inner compartment parameter, a tool housing parameter, aborehole fluid parameter, a borehole casing parameter, a fractureparameter, and a surrounding formation region parameter.

This approach enables the use of continuous energy cross-section data.This allows avoidance of the many problems that one meets when applyingdiffusion or discrete ordinate (or some Monte Carlo) neutron transportcodes, such as the need to define an energy group structure. The resultof using multi-group approaches is often an inability to quantifycertainty or confidence in the obtained results, as the cross-sectionsfor most neutron reactions (whose rates we wish to obtain) are highlydependent on the energy of the neutron. In accordance with thecontinuous energy cross-section approach, we simply apply the value ofthe appropriate cross-sections at the current Monte Carlo neutron'senergy whenever it passes through a region of interest. By samplinglarge numbers of neutron tracks, we obtain an estimate of aggregateneutron behavior. Particular attention is given to the production ofV-52 (if using vanadium as the radiation susceptible material) andwhatever other isotope is deemed pertinent. Estimates of the rates ofpertinent reactions in finite volumes with indexed positions are thenobtained. These are essentially the nuclide production rates as afunction of position relative to the source, that will be used in theradionuclide buildup and decay model component. To understand thedetails of the radionuclide buildup and decay model, it is important tonote that in this case all the finite volumes are set to 1 cm in thevertical dimension. The neutron transport model is key to finding thequantitative relationship between the tag concentration and the fracturewidth. It is also important for determining spatial distributions ofother activation products so that we can get good signatures for the LLScalculation. It is noted that the library spectra changeshape—especially at low energies—when they are spatially distributed indifferent ways.

The main assumption of the neutron transport model is that thesteady-state neutron flux simply follows along as the source moves uptoward the surface, and a more complicated temporal adjustment is notnecessary. This assumption can be made because time-dependent neutronpopulation effects will not be important unless the desired loggingspeed is above 250 cm/second, which in most cases it is not as speedsthat fast will not be suitable due to insufficient neutron exposure ofthe radiation susceptible proppant.

The loss rates for radio-nuclides are the product of the decay constantand the instantaneous population; it is this law that leads to thefamiliar characteristics of exponential decay. The radio-nuclide buildupand decay model uses the implicit or backward Euler method tonumerically integrate the variable source neutron activation problem.Let a finite volume element be indexed by radial and axial indices i andj. The concentration C(t) of a given nuclide in volume element i,j isobtained by numerically integrating the variable neutron sourceactivation equation:

$\frac{C}{t_{i,j}} = {{{production}\mspace{14mu} {rate}_{i,j}} - {{loss}\mspace{14mu} {rate}_{i,j}}}$$\frac{C}{t_{i,j}} = {{( {N\; {\sigma\varphi}} )(t)_{i,j}} - {\lambda \; {C(t)}_{i,j}}}$

(Nσφ)(t)_(i,j) represents the rate of production in volume element i,jtaking into account the concentration of the target nuclide, theenergy-dependent neutron cross-section, and the energy-dependent neutronflux. The production rate is derived from the neutron transport moduleresults. λ represents the decay constant of the radionuclide whoconcentration is C.

As the source moves past volume element i,j the production rate changes.So, the value of C is obtained for the instant when the neutron sourcehas receded far enough away that production is no longer significant. Inour first iteration this distance has been taken as 20 cm. So theequation above is numerically integrated over a 40 second exposure to avariable neutron source. The 40 seconds covers the 20 cm above and 20 cmbelow the source at a 1 cm/s logging speed. The exposure time is thedistance divided by the logging speed (the variable ‘vel’). The implicitEuler method can be applied, for example, using the following lines ofFORTRAN code:

DO i=0,13 DO k=19,0,−1 ic0(i)=ic0(i)+n_sig_phi(i,k)/vel−lam*ic0(i)/velENDDO DO k=0,19,1 ic0(i)=ic0(i)+n_sig_phi(i,k)/vel−lam*ic0(i)/vel ENDDOENDDO

The variable ‘ic0’ is the concentration at the instant the productionrate is deemed no longer important. It is only a function of radialdistance since all axial indices at the same radial distance will havethe same instantaneous concentration at this instant, but the instantthat each axial index reaches this concentration does not occur at thesame time. The variables ‘n_sig_phi’ and ‘lam’ represent the productionrates and decay constants respectively. To obtain the concentrationssurrounding the spectrometer the following lines of FORTRAN code can beused:

DO k=0,39 decfac(k)=exp(−lam*(sd/vel+20.−REAL(k)/vel)) DO i=0,13 c(i,k)= ic0(i)*decfac(k)  IF (k<=19) THEN WRITE(*,*) “x= ”,xyz(1,i), “z= ”,xyz(3,k)−sd, “c= ”, c(i,k), “dec= ”, decfac(k) ELSE WRITE(*,*) “x=”,xyz(1,i), “z= ”, xyz(3,k−20)+20−sd, “c= ”, c(i,k), “dec= ”, decfac(k)ENDIF ENDDO ENDDO

Where the c variable holds the concentration as a function of position,but the position indices are now for the position relative to thespectrometer position rather than the source position. This calculationis very similar to the implicit Euler method used to get the value ofic0, but with zero production rate. The variable sd is thesource-detector spacing, taken initially to be 526.8 cm.

Concentrations of radio-nuclides that are present when the loggingtool's lower spectrometer reaches a given position are then obtained byintegrating (numerically) the instantaneous production rates and lossrates as the neutron source moves past that given position. Theconcentration of radio-nuclides surrounding the detector is transformedinto a gamma-ray source term using basic nuclear data for gamma-rayemission. The gamma-ray source term is used in a photon transportcalculation to determine the response of the spectrometer. What weaccomplish by all these transformations and calculations is an estimateof the lower detector response for an assumed borehole environment.

Again, here MCNP5 is used to solve the radiation transport problem, onlynow using a gamma ray source derived from the position-dependentconcentrations calculated in the radio-nuclide buildup and decay module,instead of neutron source. Energy deposition is tallied in thespectrometer for each simulated history to get an estimate of aggregatebehavior that determines the observed spectrum. However, the Monte Carlocalculation does not take into account many of the inherentimperfections of a spectrometer. To obtain a less idealistic and morerealistic spectrum, it may be also necessary to apply a response modelfor the spectrometer, essentially to spread out the spectrum to getrealistically broad peaks that accurately simulate the behavior observedin a physical spectrometer.

The end result of the modeling system provides an expected spectrum fora given borehole environment and fracture size. By comparing an observedspectrum to a database of expected predicted calculated spectra forconditions similar to those of the fracture under measurement, anaccurate estimate of the fracture geometry can be obtained.

While the invention has been described with reference to exemplaryembodiments, it will be understood by those skilled in the art thatvarious changes may be made and equivalents may be substituted forelements thereof without departing from the scope of the invention. Inaddition, many modifications may be made to adapt a particular situationor material to the teachings of the invention without departing from theessential scope thereof. Therefore, it is intended that the inventionnot be limited to the particular embodiment disclosed as the best modecontemplated for carrying out this invention, but that the inventionwill include all embodiments falling within the scope of the appendedclaims.

1. A method of determining fracture geometry of a subterranean formationfrom radiation emitted from a fracture in said formation, comprising: a)measuring gamma-radiation emitted from the fracture; b) subtractingbackground radiation from said measured gamma-radiation to obtain apeak-energy measurement; c) comparing said peak-energy measurement witha gamma-ray transport/spectrometer response model; and d) determiningformation fracture geometry of said fracture in accordance with valuesassociated with said response model.
 2. The method of claim 1, furthercomprising generating said gamma-ray transport/spectrometer responsemodel by applying a Monte Carlo simulation to gamma-ray buildup/decayprofile data.
 3. The method of claim 2, wherein said Monte Carlosimulation comprises a Monte Carlo N-Particle Transport Code.
 4. Themethod of claim 2, wherein said gamma-ray buildup/decay profile data isobtained by integrating neutron transport data.
 5. The method of claim4, wherein said integrating is performed using a Euler method.
 6. Themethod of claim 5, wherein said Euler method is an implicit Eulermethod.
 7. The method of claim 5, wherein said Euler method is abackward Euler method.
 8. The method of claim 5, wherein said neutrontransport data is obtained by applying neutron source parameters andsubterranean formation parameters to a Monte Carlo simulation.
 9. Themethod of claim 8, wherein said neutron source parameters includeneutron source, tool composition, tool geometry, and said subterraneanformation parameters include borehole fluid composition and formationcomposition.
 10. The method of claim 8, wherein said Monte Carlosimulation comprises a Monte Carlo N-Particle Transport Code.
 11. Themethod of claim 1, wherein fracture geometry includes the height andwidth of a fracture formation.
 12. A method for modeling geometricalparameters of a subterranean formation fracture detected by collectinggamma-radiation data stimulated by a neutron source, comprising: a)obtaining neutron transport data by applying neutron source detectorparameters and subterranean formation parameters to a Monte Carlosimulation; b) obtaining gamma-ray buildup/decay profile data byintegrating said neutron transport data; c) generating a gamma-raytransport/spectrometer response model by applying a Monte Carlosimulation to said gamma-ray buildup/decay profile data; and d) creatinga gamma-ray transport/spectrometer response database correlatinggamma-radiation spectra with subterranean formation fracture geometryparameters.
 13. The method of claim 12, wherein said Monte Carlosimulations comprise a Monte Carlo N-Particle Transport Code.
 14. Themethod of claim 12, wherein said integrating is performed using a Eulermethod.
 15. The method of claim 14, wherein said Euler method is animplicit Euler method.
 16. The method of claim 14, wherein said Eulermethod is a backward Euler method.
 17. The method of claim 12, whereinsaid neutron source parameters include neutron source, tool composition,tool geometry, and said subterranean formation parameters includeborehole fluid composition and formation composition.
 18. A method ofdetermining fracture geometry of a subterranean formation from radiationemitted from a fracture in said formation, comprising: a) measuringgamma-radiation emitted from the fracture using a logging tool havingtwo radiation detectors, wherein one of said two radiation detectors isused to measure background radiation emissions; b) subtractingbackground radiation from said measured gamma-radiation to obtain apeak-energy measurement; c) comparing said peak-energy measurement witha gamma-ray transport/spectrometer response model; and d) determiningformation fracture geometry of said fracture in accordance with valuesassociated with said response model.
 19. A method as set forth in claim18, wherein peak-energy of gamma radiation is received by said detectorsas a result of activation of a radiation susceptible material in saidfracture, and said one of said two radiation detectors receivesradiation present in said subterranean formation before and after saidactivation.
 20. A method as set forth in claim 19, wherein saidactivation is performed by bombardment of said radiation susceptiblematerial with neutrons from a neutron source attached to said detectors.